Be Star Disk Models in Consistent Vertical Hydrostatic Equilibrium

TL;DR

This paper improves Be star disk models by enforcing vertical hydrostatic equilibrium, revealing significant differences from previous fixed-density models, especially in high-density, cool disk regions, and establishing a relation between disk temperature and stellar type.

Contribution

It introduces a modified { extsc{bedisk}} code that enforces consistent hydrostatic equilibrium, improving the physical accuracy of Be star disk models.

Findings

Fixed models differ substantially from hydrostatic models at high densities.

Cool equatorial regions develop in dense disks, affecting observable properties.

An approximate relation between disk temperature and stellar effective temperature is established.

Abstract

A popular model for the circumstellar disks of Be stars is that of a geometrically thin disk with a density in the equatorial plane that drops as a power law of distance from the star. It is usually assumed that the vertical structure of such a disk (in the direction parallel to the stellar rotation axis) is governed by the hydrostatic equilibrium set by the vertical component of the star's gravitational acceleration. Previous radiative equilibrium models for such disks have usually been computed assuming a fixed density structure. This introduces an inconsistency as the gas density is not allowed to respond to temperature changes and the resultant disk model is not in vertical, hydrostatic equilibrium. In this work, we modify the {\sc bedisk} code of \citet{sig07} so that it enforces a hydrostatic equilibrium consistent with the temperature solution. We compare the disk densities, temperatures, H$\alpha$ line profiles, and near-IR excesses predicted by such models with those computed from models with a fixed density structure. We find that the fixed models can differ substantially from the consistent hydrostatic models when the disk density is high enough that the circumstellar disk develops a cool ($T\lesssim10,000 $K) equatorial region close to the parent star. Based on these new hydrostatic disks, we also predict an approximate relation between the (global) density-averaged disk temperature and the $T_{\rm eff}$ of the central star, covering the full range of central Be star spectral types.